The Five-Percent Rule

Common practice among system designers is to design for a wire resistance of no more than 5% of the loudspeaker’s minimum impedance. Using the example of a 4 ohm loudspeaker, the maximum tolerable wire resistance becomes:

Any combination of wire length and area can be used as long as the loop resistance does not exceed this value. Figure 3 shows the resistance per unit of some common wire gauges.

 By limiting the loop resistance to 5-percent of the loudspeaker’s impedance, the level change due to line loss will be limited to 0.5 dB, since:

Line losses may be calculated by using the Syn-Aud-Con Slide Rule or the Syn-Aud-Con System Design Spreadsheet. Both are included in the course materials for Syn-Aud-Con Seminars.

Damping Factor

A loudspeaker cone has both mass and inertia, and like any moving body it tends to oppose any action to brake its motion. Damping factor is an indicator of how well an amplifier can damp the tendancy of a loudspeaker to ring after the cessation of a stimulus.

A simple experiment illustrates the concept(2). Take a 12” or 15” woofer and sharply press-in on the cone. It should move easily. “Thump” it with your finger and note the cone motion. Now, short the terminals on the woofer and repeat the experiment. You will notice that the cone is much harder to displace, and doesn’t “ring” as much when “thumped.” Shorting the terminals has allowed the loudspeaker to damp itself by the current generated in the voice coil by the motion of the cone. This “back EMF” is useful for reducing the tendancy of a cone driver to ring. An amplifier with a very low output impedance can perform the same function as the short. The damping factor of an amplifier/loudspeaker combination is formed by the ratio of the loudspeaker’s impedance to the amplifier’s output impedance. Numbers in the hundreds are often quoted on spec sheets, but in the real world the resistance of the loudspeaker cable must be included with the amplifier’s output impedance. Excessive cable resistance effectively offsets the “short” between the loudspeaker terminals presented by the amplifier. In practice, the five-percent rule for calculating the wire gauge will produce a damping factor of about 20 - more than sufficient for sound reinforcement systems. Figure 4 illustrates the reduction of damping in an extreme case that produced a subtle (but measurable) audible change in woofer performance.

“Good Sounding” Wire

Changes in sound quality are often attributed to the loudspeaker cable. Frequency-dependent level changes can be caused by the wire resistance. This is due to the complex nature of a loudspeaker’s impedance(3).

Figure 5 shows the impedance curve of a loudspeaker in a tuned-box. Note that the impedance is a function of frequency. As shown earlier, the amplifier/loudspeaker interface is of the constant-voltage type. This means that the voltage delivered to the loudspeaker by the amplifier will be largely independent of frequency. Therefore the current drawn by a loudspeaker will depend upon the magnitude of the impedance at any given frequency, and increased current will be supplied to the loudspeaker at “low spots” on the impedance curve, resulting in greater input power to the loudspeaker. An increase in resistance caused by the loudspeaker wire will have a greater effect on power drawn at “low spots” on the curve than at peaks. This can cause a frequency-dependent change in what is heard by the listener. Since the power reduction is greatest in the low-mid region (usually the lowest impedance region of the curve), the subjective impression is that of “tighter” bass response. As with damping factor, following the five-percent rule when calculating the required wire gauge will minimize such changes.

Other Issues

There are other issues that determine the best cable type for an application.
- It is usually advantageous to use stranded wire rather than solid. The reasons are more practical than audible - solid wire is more difficult to pull and terminate.
- Twisted-pair wires offer the advantage of reduced magnetic field radiation into other wires or nearby equipment.
- The jacket material must have the proper fire rating to assure that it doesn’t emit noxious fumes when burnt. Consult the code books before specifying wire!

Conclusion

The most significant aspect of the amplifier/ loudspeaker interface is the loudspeaker wire, and the most significant parameter of the wire is its resistance. It’s always better to use shorter wire of larger diameter to minimize this resistance.

Other factors such as capacitance and inductance can affect the performance of a system if they get out of control. I urge the reader to test the significance these effects for themselves rather than relying on the conclusions or claims of others. Much confusion can arise from exaggerating the significance of wire parameters.

The amplifier/loudspeaker interface is but one of many interfaces in an audio system. The five-percent rule provides a useful metric for assuring that it is not degraded by excessive wire resistance.

References:
(1) The ARRL Handbook for Radio Amateurs p. 6.23 -Seventy-seventh edition 1999
(2) Testing Loudspeakers by Joseph D’Appolito
(3) Sound System Engineering Second Edition by Don and Carolyn Davis

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